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  1. added 2018-12-22
    Plato’s Philosophy of Cognition by Mathematical Modelling.Roman S. Kljujkov & Sergey Kljujkov - 2014 - Dialogue and Universalism 24 (3):110-115.
    By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long time, (...)
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  2. added 2018-12-03
    Uwagi o arytmetyce Grassmanna.Jerzy Hanusek - 2015 - Diametros 45:107-121.
    Hermann Grassmann’s 1861 work [2] was probably the first attempt at an axiomatic approach to arithmetic. The historical significance of this work is enormous, even though the set of axioms has proven to be incomplete. Basing on the interpretation of Grassmann’s theory provided by Hao Wang in [4], I present its detailed discussion, define the class of models of Grassmann’s arithmetic and discuss a certain axiom system for integers, modeled on Grassmann’s theory. At the end I propose to modify the (...)
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  3. added 2018-10-31
    What Isn’T Obvious About ‘Obvious’: A Data-Driven Approach to Philosophy of Logic.Moti Mizrahi - forthcoming - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Press. pp. 201-224.
    It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, I propose that systematically (...)
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  4. added 2018-10-16
    Part 3: Programming Atomic and Gravitational Orbitals in a Simulation Hypothesis.Malcolm J. Macleod - manuscript
    This article introduces a method for programming orbitals at the Planck level. Mathematical probability orbitals are replaced with units of `orbit momentum' with orbital regions derived from geometrical imperatives rather than abstract forces. In this approach the electron does not orbit around a nucleus but rather is maintained within an orbital region by the confines of the geometry of the orbital (this orbit momentum is the orbital). There is no electron transition between orbitals, rather the existing orbital is exchanged for (...)
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  5. added 2018-08-25
    Part 2: Relativity in a Planck-Level Black-Hole Universe Simulation, a Simulation Hypothesis.Malcolm Macleod - manuscript
    The Simulation Hypothesis proposes that all of reality is in fact an artificial simulation, analogous to a computer simulation, and as such our reality is an illusion. Outlined here is a method for reproducing relativistic mass, space and time from the Planck level. For a virtual universe the model uses a 4-axis hyper-sphere that expands in incremental steps (the simulation clock-rate). Virtual particles that oscillate between an electric wave-state and a mass point-state are mapped within this hyper-sphere, the oscillation driven (...)
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  6. added 2018-08-25
    Programming Planck Units From a Virtual Electron; a Simulation Hypothesis.Malcolm J. Macleod - 2018 - European Physical Journal Plus 133:278.
    The simulation hypothesis proposes that all of reality is an artificial simulation. In this article I describe a simulation model that derives Planck level units as geometrical forms from a virtual (dimensionless) electron formula $f_e$ that is constructed from 2 unit-less mathematical constants; the fine structure constant $\alpha$ and $\Omega$ = 2.00713494... ($f_e = 4\pi^2r^3, r = 2^6 3 \pi^2 \alpha \Omega^5$). The mass, space, time, charge units are embedded in $f_e$ according to these ratio; ${M^9T^{11}/L^{15}} = (AL)^3/T$ (units = (...)
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  7. added 2018-07-30
    New Essays on Frege: Between Science and Literature.Gisela Bengtsson, Simo Säätelä & Alois Pichler (eds.) - 2018 - Springer.
    This volume collects nine essays that investigate the work of Gottlob Frege. The contributors address Frege’s work in relation to literature and fiction (Dichtung), the humanities (Geisteswissenschaften), and science (Wissenschaft). Overall, the essays consider internal connections between different aspects of Frege’s work while acknowledging the importance of its philosophical context. -/- There are also further common strands between the papers, such as the relation between Frege’s and Wittgenstein’s approaches to philosophical investigations, the relation between Frege and Kant, and the place (...)
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  8. added 2018-06-07
    Lautman on Problems as the Conditions of Existence of Solutions.Simon B. Duffy - 2018 - Angelaki 23 (2):79-93.
    Albert Lautman (b. 1908–1944) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that: ‘in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe’ (Lautman 2011, 87). He goes on to characterize this (...)
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  9. added 2018-05-24
    Hermann von Helmholtz's Mechanism: The Loss of Certainty. A Study on the Transition From Classical to Modern Philosophy of Nature.Gregor Schiemann - 2009 - Springer.
    Two seemingly contradictory tendencies have accompanied the development of the natural sciences in the past 150 years. On the one hand, the natural sciences have been instrumental in effecting a thoroughgoing transformation of social structures and have made a permanent impact on the conceptual world of human beings. This historical period has, on the other hand, also brought to light the merely hypothetical validity of scientific knowledge. As late as the middle of the 19th century the truth-pathos in the natural (...)
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  10. added 2018-03-22
    A (Possibly) New Kind of Euclidean Geometry Based on an Idea by Mary Pardoe.Aaron Sloman - manuscript
    For over half a century I have been interested in the role of intuitive spatial reasoning in mathematics. My Oxford DPhil Thesis (1962) was an attempt to defend Kant's philosophy of mathematics, especially his claim that mathematical proofs extend our knowledge (so the knowledge is "synthetic", not "analytic") and that the discoveries are not empirical, or contingent, but are in an important sense "a priori" (which does not imply "innate") and also necessarily true. -/- I had made my views clear (...)
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  11. added 2018-02-17
    B. Buldt, B. Löwe and T. Müller (Eds.), Special Issue Towards a New Epistemology of Mathematics; B. Löwe and T. Müller (Eds.), PhiMSAMP: Philosophy of Mathematics: Sociological Aspects and Mathematical Practice; K. François, B. Löwe, T. Müller and B. Van Kerkhove (Eds.), Foundations of the Formal Sciences VII: Bringing Together Philosophy and Sociology of Science. [REVIEW]Robert Thomas - 2012 - Philosophia Mathematica 20 (2):258-260.
  12. added 2018-02-17
    Wittgenstein Sobre as Provas Indutivas.André Porto - 2009 - Dois Pontos 6 (2).
    This paper offers a reconstruction of Wittgenstein's discussion on inductive proofs. A "algebraic version" of these indirect proofs is offered and contrasted with the usual ones in which an infinite sequence of modus pones is projected.
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  13. added 2018-02-17
    Logica Universalis: Towards a General Theory of Logic.Jean-Yves Béziau (ed.) - 2007 - Birkhäuser Basel.
    Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last (...)
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  14. added 2018-02-17
    Remarks on Peano Arithmetic.Charles Sayward - 2000 - Russell: The Journal of Bertrand Russell Studies 20 (1):27-32.
    Russell held that the theory of natural numbers could be derived from three primitive concepts: number, successor and zero. This leaves out multiplication and addition. Russell introduces these concepts by recursive definition. It is argued that this does not render addition or multiplication any less primitive than the other three. To this it might be replied that any recursive definition can be transformed into a complete or explicit definition with the help of a little set theory. But that is a (...)
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  15. added 2018-02-17
    Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford University Press.
    Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic (...)
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  16. added 2017-12-04
    Wittgenstein’s Philosophy of Mathematics: Felix Mühlhölzer in Conversation with Sebastian Grève.Sebastian Grève & Felix Mühlhölzer - 2014 - Nordic Wittgenstein Review 3 (2):151-180.
    Sebastian Grève interviews Felix Mühlhölzer on his work on the philosophy of mathematics.
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  17. added 2017-09-26
    For a Topology of Dynamical Systems.Claudio Mazzola & Marco Giunti - 2016 - In Gianfranco Minati, Mario Abram & Eliano Pessa (eds.), Towards a Post-Bertalanffy Systemics. Springer. pp. 81-87.
    Dynamical systems are mathematical objects meant to formally capture the evolution of deterministic systems. Although no topological constraint is usually imposed on their state spaces, there is prima facie evidence that the topological properties of dynamical systems might naturally depend on their dynamical features. This paper aims to prepare the grounds for a systematic investigation of such dependence, by exploring how the underlying dynamics might naturally induce a corresponding topology.
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  18. added 2017-08-23
    ‘Chasing’ The Diagram - The Use of Visualizations in Algebraic Reasoning.Silvia De Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
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  19. added 2017-07-07
    Whitehead and Pythagoras.Arran Gare - 2006 - Concrescence 7:3 - 19.
    While the appeal of scientific materialism has been weakened by developments in theoretical physics, chemistry and biology, Pythagoreanism still attracts the allegiance of leading scientists and mathematicians. It is this doctrine that process philosophers must confront if they are to successfully defend their metaphysics. Peirce, Bergson and Whitehead were acutely aware of the challenge of Pythagoreanism, and attempted to circumvent it. The problem addressed by each of these thinkers was how to account for the success of mathematical physics if the (...)
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  20. added 2017-06-21
    A Not So Fine Modal Version of Generality Relativism.Gonçalo Santos - 2010 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 25 (2):149-161.
    The generality relativist has been accused of holding a self-defeating thesis. Kit Fine proposed a modal version of generality relativism that tries to resist this claim. We discuss his proposal and argue that one of its formulations is self-defeating.
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  21. added 2017-05-22
    Proof Phenomenon as a Function of the Phenomenology of Proving.Inês Hipólito - 2015 - Progress in Biophysics and Molecular Biology 119:360-367.
    Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)”. This “exact replica” brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical proving (...)
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  22. added 2017-03-06
    Forms of Mathematization (14th-17th Centuries).Sophie Roux - 2010 - Early Science and Medicine 15 (4):319-337.
    According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. This grand narrative began with the exhibition of quantitative laws that these heroes, Galileo and Newton for example, had disclosed: the law of falling bodies, according to which the speed of a falling body is proportional to the square of the time that has elapsed since the beginning of its fall; the (...)
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  23. added 2017-02-16
    REINHARDT, KURT F. "A Realistic Philosophy". [REVIEW]C. L. Bonnet - 1944 - Modern Schoolman 22:173.
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  24. added 2017-02-15
    Philosophies and Pedagogies of Mathematics.Boris Handal - 2003 - Philosophy of Mathematics Education Journal 17.
  25. added 2017-02-15
    A Logical Journey. From Gödel To Philosophy. [REVIEW]Eckehart Köhler - 1999 - Vienna Circle Institute Yearbook 6:312-318.
    Hao Wang was born in 1921 in north-east China of a westernizing father; he came to study and teach at Harvard in 1949, and he remained in the West, always feeling culturally of two distinct worlds. His deep interest in Gödel as thinker and person indicates a Confucian influence, which holds the teacher to be the great authority in both administrative as well as family matters. Wang more than once combined scientific explication with biography, since in China a student must (...)
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  26. added 2017-02-15
    The Principles of Mathematics Revisited. [REVIEW]O. Bradley Bassler - 1997 - Review of Metaphysics 51 (2):424-425.
  27. added 2017-02-15
    Notes on Philosophy, Probability and Mathematics. Frank Plumpton Ramsey, Maria Carla Galavotti.Frank Plumpton Ramsey & Maria Concetta Di Maio - 1994 - Philosophy of Science 61 (3):487.
  28. added 2017-02-14
    Ontological Reductions in Mathematics. Part III: On Reconstruction of Some Parts of Mathematics.Krzysztof Wojtowicz - 2011 - Filozofia Nauki 19 (3):49.
  29. added 2017-02-14
    (Implications of Experimental Mathematics Jor the Philosoj) Hij of Mathematics1.Jonathan Borwein - 2008 - In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 33.
  30. added 2017-02-14
    Mathematics, Metaphysics, Philosophy'.Jean-Michel‘Idea Salanskis - 2006 - In Simon B. Duffy (ed.), Virtual Mathematics: The Logic of Difference. Clinamen.
  31. added 2017-02-14
    312 Teodors Celms, Kurt Stavenhagen and Phenomenology in Latvia.Givi Margvelashvili - 2003 - In Anna-Teresa Tymieniecka (ed.), Phenomenology World-Wide. Kluwer Academic Publishers. pp. 80--311.
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  32. added 2017-02-14
    Philosophies of Mathematics.James Robert Brown - 2002 - Mind 111 (444):860-862.
  33. added 2017-02-14
    A Bibliography of Hao Wang.Marie Grossi, Montgomery Link, Katalin Makkai & Charles Parsons - 1998 - Philosophia Mathematica 6 (1):25-38.
    A listing is given of the published writings of the logician and philosopher Hao Wang , which includes all items known to the authors, including writings in Chinese and translations into other languages.
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  34. added 2017-02-13
    Teodors Celms, Kurt Stavenhagen and Phenomenology in Latvia.E. Buceniece - 2002 - Analecta Husserliana 80:312-315.
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  35. added 2017-02-13
    Collected Works of Kurt Godel: Volume I.J. L. Bell & S. Feferman - 1987 - Philosophical Quarterly 37 (147):216.
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  36. added 2017-02-13
    Mathematics as a Critical Enterprise.Peggy Marchi - 1976 - In R. S. Cohen, P. K. Feyerabend & M. Wartofsky (eds.), Essays in Memory of Imre Lakatos. Reidel. pp. 379--393.
  37. added 2017-02-13
    Godel's Proof.S. R. Peterson, Ernest Nagel & James R. Newman - 1958 - Philosophical Quarterly 11 (45):379.
    In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy (...)
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  38. added 2017-02-12
    Reflections on" Wang's Paradox".John Burgess - 2013 - Teorema: International Journal of Philosophy 32 (1):125-139.
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  39. added 2017-02-12
    Measure – From Mathematics to Ethics.Luka Boršić - 2007 - Filozofska Istrazivanja 27 (4):751-764.
  40. added 2017-02-12
    Poincaré and the Philosophy of Mathematics.A. W. Moore - 1993 - Philosophical Books 34 (3):191-192.
  41. added 2017-02-11
    Notes on Philosophy, Probability and Mathematics.Frank Plumpton Ramsey & E. J. Lowe - 1997 - British Journal for the Philosophy of Science 48 (2):300-301.
  42. added 2017-02-09
    Kurt F. Leidecker 1902-1991.George M. Van Sant - 1992 - Proceedings and Addresses of the American Philosophical Association 65 (7):32 - 33.
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  43. added 2017-02-08
    Monads and Mathematics: Gödel and Husserl.Richard Tieszen - 2012 - Axiomathes 22 (1):31-52.
    In 1928 Edmund Husserl wrote that “The ideal of the future is essentially that of phenomenologically based (“philosophical”) sciences, in unitary relation to an absolute theory of monads” (“Phenomenology”, Encyclopedia Britannica draft) There are references to phenomenological monadology in various writings of Husserl. Kurt Gödel began to study Husserl’s work in 1959. On the basis of his later discussions with Gödel, Hao Wang tells us that “Gödel’s own main aim in philosophy was to develop metaphysics—specifically, something like the monadology of (...)
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  44. added 2017-02-08
    Editor's Introduction: Hungarian Studies in Lakatos' Philosophies of Mathematics and Science.Stefania R. Jha - 2006 - Perspectives on Science 14 (3):257-262.
  45. added 2017-02-08
    Harmless Naturalism: The Limits of Science and the Nature of Philosophy. [REVIEW]Andrew D. Cling - 2001 - Philosophy and Phenomenological Research 62 (2):493-495.
  46. added 2017-02-08
    Ethics and Mathematics. Intuitive Thinking in Cantor, Gödel and Steiner.Reiner Wimmer - 1987 - Philosophy and History 20 (1):36-36.
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  47. added 2017-02-08
    Reflections on Gôdel.Hao Wang - 1987 - MIT Press.
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  48. added 2017-02-02
    A Logical Journey. From Gödel to Philosophy by Hao Wang. MIT Press, Cambridge, Mass., 1996, Pp. XI+391.Colin Howson - 1998 - Philosophy 73 (3):495-523.
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  49. added 2017-02-01
    On Wittgenstein's Philosophy of Mathematics.James Conant - 1997 - Proceedings of the Aristotelian Society 97 (2):195–222.
  50. added 2017-02-01
    Kurt Godel and Phenomenology.Richard Tieszen - 1992 - Philosophy of Science 59 (2):176-194.
    Godel began to seriously study Husserl's phenomenology in 1959, and the Godel Nachlass is known to contain many notes on Husserl. In this paper I describe what is presently known about Godel's interest in phenomenology. Among other things, it appears that the 1963 supplement to "What is Cantor's Continuum Hypothesis?", which contains Godel's famous views on mathematical intuition, may have been influenced by Husserl. I then show how Godel's views on mathematical intuition and objectivity can be readily interpreted in a (...)
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1 — 50 / 595